Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
Nonstandard Analysis
Download Nonstandard Analysis full books in PDF, epub, and Kindle. Read online Nonstandard Analysis ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Non-standard Analysis by : Abraham Robinson
Download or read book Non-standard Analysis written by Abraham Robinson and published by Princeton University Press. This book was released on 2016-08-11 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.
Book Synopsis Lectures on the Hyperreals by : Robert Goldblatt
Download or read book Lectures on the Hyperreals written by Robert Goldblatt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers, but as a radically different way of viewing many standard mathematical concepts and constructions. It is a source of new ideas, objects and proofs, and a wealth of powerful new principles of reasoning. The book begins with the ultrapower construction of hyperreal number systems, and proceeds to develop one-variable calculus, analysis and topology from the nonstandard perspective. It then sets out the theory of enlargements of fragments of the mathematical universe, providing a foundation for the full-scale development of the nonstandard methodology. The final chapters apply this to a number of topics, including Loeb measure theory and its relation to Lebesgue measure on the real line. Highlights include an early introduction of the ideas of internal, external and hyperfinite sets, and a more axiomatic set-theoretic approach to enlargements than is usual.
Book Synopsis Nonstandard Analysis for the Working Mathematician by : Peter A. Loeb
Download or read book Nonstandard Analysis for the Working Mathematician written by Peter A. Loeb and published by Springer. This book was released on 2015-08-26 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with a simple formulation accessible to all mathematicians, this second edition is designed to provide a thorough introduction to nonstandard analysis. Nonstandard analysis is now a well-developed, powerful instrument for solving open problems in almost all disciplines of mathematics; it is often used as a ‘secret weapon’ by those who know the technique. This book illuminates the subject with some of the most striking applications in analysis, topology, functional analysis, probability and stochastic analysis, as well as applications in economics and combinatorial number theory. The first chapter is designed to facilitate the beginner in learning this technique by starting with calculus and basic real analysis. The second chapter provides the reader with the most important tools of nonstandard analysis: the transfer principle, Keisler’s internal definition principle, the spill-over principle, and saturation. The remaining chapters of the book study different fields for applications; each begins with a gentle introduction before then exploring solutions to open problems. All chapters within this second edition have been reworked and updated, with several completely new chapters on compactifications and number theory. Nonstandard Analysis for the Working Mathematician will be accessible to both experts and non-experts, and will ultimately provide many new and helpful insights into the enterprise of mathematics.
Book Synopsis Nonstandard Analysis by : Alain Robert
Download or read book Nonstandard Analysis written by Alain Robert and published by Courier Corporation. This book was released on 2003-01-01 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise text is based on the axiomatic internal set theory approach. Theoretical topics include idealization, standardization, and transfer, real numbers and numerical functions, continuity, differentiability, and integration. Applications cover invariant means, approximation of functions, differential equations, more. Exercises, hints, and solutions. "Mathematics teaching at its best." — European Journal of Physics. 1988 edition.
Book Synopsis Nonstandard Analysis in Practice by : Francine Diener
Download or read book Nonstandard Analysis in Practice written by Francine Diener and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the graduate mathematician and researcher to the effective use of nonstandard analysis (NSA). It provides a tutorial introduction to this modern theory of infinitesimals, followed by nine examples of applications, including complex analysis, stochastic differential equations, differential geometry, topology, probability, integration, and asymptotics. It ends with remarks on teaching with infinitesimals.
Book Synopsis Nonstandard Analysis by : Martin Väth
Download or read book Nonstandard Analysis written by Martin Väth and published by Springer Science & Business Media. This book was released on 2007 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces Robinson's nonstandard analysis, an application of model theory in analysis. Unlike some texts, it does not attempt to teach elementary calculus on the basis of nonstandard analysis, but points to some applications in more advanced analysis. The contents proceed from a discussion of the preliminaries to Nonstandard Models; Nonstandard Real Analysis; Enlargements and Saturated Models; Functionals, Generalized Limits, and Additive Measures; and finally Nonstandard Topology and Functional Analysis. No background in model theory is required, although some familiarity with analysis, topology, or functional analysis is useful. This self-contained book can be understood after a basic calculus course.
Book Synopsis An Introduction to Nonstandard Real Analysis by : Albert E. Hurd
Download or read book An Introduction to Nonstandard Real Analysis written by Albert E. Hurd and published by Academic Press. This book was released on 1985-10-01 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to make Robinson's discovery, and some of the subsequent research, available to students with a background in undergraduate mathematics. In its various forms, the manuscript was used by the second author in several graduate courses at the University of Illinois at Urbana-Champaign. The first chapter and parts of the rest of the book can be used in an advanced undergraduate course. Research mathematicians who want a quick introduction to nonstandard analysis will also find it useful. The main addition of this book to the contributions of previous textbooks on nonstandard analysis (12,37,42,46) is the first chapter, which eases the reader into the subject with an elementary model suitable for the calculus, and the fourth chapter on measure theory in nonstandard models.
Book Synopsis Nonstandard Analysis, Axiomatically by : Vladimir Kanovei
Download or read book Nonstandard Analysis, Axiomatically written by Vladimir Kanovei and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the aftermath of the discoveries in foundations of mathematiC's there was surprisingly little effect on mathematics as a whole. If one looks at stan dard textbooks in different mathematical disciplines, especially those closer to what is referred to as applied mathematics, there is little trace of those developments outside of mathematical logic and model theory. But it seems fair to say that there is a widespread conviction that the principles embodied in the Zermelo - Fraenkel theory with Choice (ZFC) are a correct description of the set theoretic underpinnings of mathematics. In most textbooks of the kind referred to above, there is, of course, no discussion of these matters, and set theory is assumed informally, although more advanced principles like Choice or sometimes Replacement are often mentioned explicitly. This implicitly fixes a point of view of the mathemat ical universe which is at odds with the results in foundations. For example most mathematicians still take it for granted that the real number system is uniquely determined up to isomorphism, which is a correct point of view as long as one does not accept to look at "unnatural" interpretations of the membership relation.
Book Synopsis Radically Elementary Probability Theory by : Edward Nelson
Download or read book Radically Elementary Probability Theory written by Edward Nelson and published by Princeton University Press. This book was released on 1987 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.
Book Synopsis Nonstandard Methods in Functional Analysis by : Siu-Ah Ng
Download or read book Nonstandard Methods in Functional Analysis written by Siu-Ah Ng and published by World Scientific. This book was released on 2010 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the early 1960s, by using techniques from the model theory of first-order logic, Robinson gave a rigorous formulation and extension of Leibniz'' infinitesimal calculus. Since then, the methodology has found applications in a wide spectrum of areas in mathematics, with particular success in the probability theory and functional analysis. In the latter, fruitful results were produced with Luxemburg''s invention of the nonstandard hull construction. However, there is still no publication of a coherent and self-contained treatment of functional analysis using methods from nonstandard analysis. This publication aims to fill this gap.
Book Synopsis Nonstandard Analysis by : Leif O. Arkeryd
Download or read book Nonstandard Analysis written by Leif O. Arkeryd and published by Springer Science & Business Media. This book was released on 1997-04-30 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im portant field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual ap proach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) invention - providing new, rich structures that are useful in modelling and representation, as well as being of interest in their own right. The aim of the present volume is to make the power and range of appli cability of NSA more widely known and available to research mathemati cians.
Book Synopsis Nonstandard Analysis and Its Applications by : Nigel Cutland
Download or read book Nonstandard Analysis and Its Applications written by Nigel Cutland and published by CUP Archive. This book was released on 1988-10-13 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an introduction to non-standard analysis and to its many applications. Non standard analysis (NSA) is a subject of great research interest both in its own right and as a tool for answering questions in subjects such as functional analysis, probability, mathematical physics and topology. The book arises from a conference held in July 1986 at the University of Hull which was designed to provide both an introduction to the subject through introductory lectures, and surveys of the state of research. The first part of the book is devoted to the introductory lectures and the second part consists of presentations of applications of NSA to dynamical systems, topology, automata and orderings on words, the non- linear Boltzmann equation and integration on non-standard hulls of vector lattices. One of the book's attractions is that a standard notation is used throughout so the underlying theory is easily applied in a number of different settings. Consequently this book will be ideal for graduate students and research mathematicians coming to the subject for the first time and it will provide an attractive and stimulating account of the subject.
Book Synopsis Abraham Robinson by : Joseph Warren Dauben
Download or read book Abraham Robinson written by Joseph Warren Dauben and published by Princeton University Press. This book was released on 2014-07-14 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most prominent mathematicians of the twentieth century, Abraham Robinson discovered and developed nonstandard analysis, a rigorous theory of infinitesimals that he used to unite mathematical logic with the larger body of historic and modern mathematics. In this first biography of Robinson, Joseph Dauben reveals the mathematician's personal life to have been a dramatic one: developing his talents in spite of war and ethnic repression, Robinson personally confronted some of the worst political troubles of our times. With the skill and expertise familiar to readers of Dauben's earlier works, the book combines an explanation of Robinson's revolutionary achievements in pure and applied mathematics with a description of his odyssey from Hitler's Germany to the United States via conflict-ridden Palestine and wartime Europe. Robinson was born in Prussia in 1918. As a boy, he fled with his mother and brother Saul to Palestine. A decade later he narrowly escaped from Paris as the Germans invaded France. Having spent the rest of World War II in England, at the Royal Aircraft Establishment in Farnborough, he began his teaching career at the Royal College of Aeronautics. Subsequently he moved to universities in Canada, Israel, and finally the United States. A joint appointment in mathematics and philosophy at UCLA led to a position at Yale University, where Robinson served as Sterling Professor of Mathematics until his untimely death at the age of fifty-five. Originally published in 1995. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Book Synopsis Applied Nonstandard Analysis by : Martin Davis
Download or read book Applied Nonstandard Analysis written by Martin Davis and published by Courier Corporation. This book was released on 2014-06-10 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This applications-oriented text assumes no knowledge of mathematical logic in its development of nonstandard analysis techniques and their applications to elementary real analysis and topological and Hilbert space. 1977 edition.
Book Synopsis Nonstandard Asymptotic Analysis by : Imme van den Berg
Download or read book Nonstandard Asymptotic Analysis written by Imme van den Berg and published by Springer. This book was released on 2006-11-15 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph considers the subject of asymptotics from a nonstandard view point. It is intended both for classical asymptoticists - they will discover a new approach to problems very familiar to them - and for nonstandard analysts but includes topics of general interest, like the remarkable behaviour of Taylor polynomials of elementary functions. Noting that within nonstandard analysis, "small", "large", and "domain of validity of asymptotic behaviour" have a precise meaning, a nonstandard alternative to classical asymptotics is developed. Special emphasis is given to applications in numerical approximation by convergent and divergent expansions: in the latter case a clear asymptotic answer is given to the problem of optimal approximation, which is valid for a large class of functions including many special functions. The author's approach is didactical. The book opens with a large introductory chapter which can be read without much knowledge of nonstandard analysis. Here the main features of the theory are presented via concrete examples, with many numerical and graphic illustrations. N
Book Synopsis Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory by : Mauro Di Nasso
Download or read book Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory written by Mauro Di Nasso and published by Springer. This book was released on 2019-05-23 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this monograph is to give an accessible introduction to nonstandard methods and their applications, with an emphasis on combinatorics and Ramsey theory. It includes both new nonstandard proofs of classical results and recent developments initially obtained in the nonstandard setting. This makes it the first combinatorics-focused account of nonstandard methods to be aimed at a general (graduate-level) mathematical audience. This book will provide a natural starting point for researchers interested in approaching the rapidly growing literature on combinatorial results obtained via nonstandard methods. The primary audience consists of graduate students and specialists in logic and combinatorics who wish to pursue research at the interface between these areas.
Book Synopsis Lectures on Non- Standard Analysis by : Moshe Machover
Download or read book Lectures on Non- Standard Analysis written by Moshe Machover and published by Springer. This book was released on 2007-01-05 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
